Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In knot theory, a branch of mathematics, a pretzel link is a special kind of link. A pretzel link which is also a knot (i.e. a link with one component) is a pretzel knot. In the standard projection of the (p_1,,p_2,dots,,p_n) pretzel link, there are p1 left-handed crossings in the first tangle, p2 in the second, and, in general, pn in the nth. A pretzel link can also be described as a Montesinos link with integer tangles. The (p_1,,p_2,dots,,p_n) pretzel link is split if at least two of the pi are zero; but the converse is false. The (-p_1,-p_2,dots,-p_n) pretzel link is the mirror image of the (p_1,,p_2,dots,,p_n) pretzel link. The (p_1,,p_2,dots,,p_n) pretzel link is link-equivalent (i.e. homotopy-equivalent in S3 to the (p_2,,p_3,dots,,p_n,,p_1) pretzel link. Thus, too, the (p_1,,p_2,dots,,p_n) pretzel link is link-equivalent to the (p_k,,p_{k+1},dots,,p_n,,p_1,,p_2,dots,,p_{k-1}) pretzel link. The (p_1,,p_2,,dots,,p_n) pretzel link is link-equivalent to the (p_n,,p_{n-1},dots,,p_2,,p_1) pretzel link.

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